Beyond Microstructures: Using the Kerr Effect to …ing polymer microstructures uses high field, high resolution 13C-nuclear magnetic resonance (NMR) spectroscopy observed in solution.

Beyond Microstructures: Using the Kerr Effect to Characterize the

Macrostructures of Synthetic Polymers

Rana Gurarslan,1 Shauntrece Hardrict,1,2 Debashish Roy,2 Casey Galvin,3 Megan R. Hill,4

Hanna Gracz,5 Brent S. Sumerlin,4 Jan Genzer,3 Alan Tonelli1

1Fiber and Polymer Science Program, North Carolina State University, Raleigh, North Carolina 276952Department of Chemistry, Southern Methodist University, Dallas, Texas 752753Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 276954Department of Chemistry, University of Florida, Gainesville, Florida 32611-72005Department of Biochemistry, North Carolina State University, Raleigh, North Carolina 27695

Correspondence to: A. E. Tonelli (E -mail: [email protected])

Received 22 July 2014; revised 29 August 2014; accepted 2 September 2014; published online 1 October 2014

DOI: 10.1002/polb.23598

ABSTRACT: The macrostructures of synthetic polymers are

essentially the complete molecular chain architectures, includ-

ing the types and amounts of constituent short-range micro-

structures, such as the regio- and stereosequences of the

inserted monomers, the amounts and sequences of monomers

found in co-, ter-, and tetra-polymers, branching, inadvertent,

and otherwise, etc. Currently, the best method for characteriz-

ing polymer microstructures uses high field, high resolution13C-nuclear magnetic resonance (NMR) spectroscopy observed

in solution. However, even 13C-NMR is incapable of determin-

ing the locations or positions of resident polymer microstruc-

tures, which are required to elucidate their complete

macrostructures. The sequences of amino acid residues in pro-

teins, or their primary structures, cannot be characterized by

NMR or other short-range spectroscopic methods, but only by

decoding the DNA used in their syntheses or, if available,

X-ray analysis of their single crystals. Similarly, there are cur-

rently no experimental means to determine the sequences or

locations of constituent microstructures along the chains of

synthetic macromolecules. Thus, we are presently unable to

determine their macrostructures. As protein tertiary and qua-

ternary structures and their resulting ultimate functions are

determined by their primary sequence of amino acids, so too

are the behaviors and properties of synthetic polymers crit-

ically dependent on their macrostructures. We seek to raise the

consciousness of both synthetic and physical polymer scien-

tists and engineers to the importance of characterizing polymer

macrostructures when attempting to develop structure–prop-

erty relations. To help achieve this task, we suggest using the

electrical birefringence or Kerr effects observed in their dilute

solutions. The molar Kerr constants of polymer solutes contrib-

uting to the birefringence of their solutions, under the applica-

tion of a strong electric field, are highly sensitive to both the

types and locations of their constituent microstructures. As a

consequence, we may begin to characterize the macrostruc-

tures of synthetic polymers by means of the Kerr effect. To

simplify implementation of the Kerr effect to characterize poly-

mer macrostructures, we suggest that NMR first be used to

determine the types and amounts of constituent microstruc-

tures present. Subsequent comparison of observed Kerr effects

with those predicted for different microstructural locations

along the polymer chains can then be used to identify the

most likely macrostructures. VC 2014 Wiley Periodicals, Inc. J.

Polym. Sci., Part B: Polym. Phys. 2015, 53, 155–166

KEYWORDS: Kerr Effect; microstructure; NMR; structural charac-

terization; structure-property relations

INTRODUCTION The schematic homopolymer stereosequen-ces (left) and comonomer sequences (right) drawn belowhave equivalent triad microstructures, that is, the samenumbers of mm, mr, rr stereosequences and •••, ••�, •�•,•��, �•�, �� comonomer sequences, but distinct macro-structures. Solution 13C-nuclear magnetic resonance(NMR), currently the best analytical method, can usuallysuccessfully identify and quantify such short-range micro-

structural elements.1,2 However, due to its relativelyshort-range, local sensitivity, NMR, including 13C-NMR, can-not determine the exact location of these microstructuralelements along the polymer backbone, nor can it reveal ifall chains in the observed polymer sample possessthe same types and amounts of microstructures or if theyare distributed nonuniformly along or among the samplechains.

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This begs the question of whether or not there is an experi-mental means that can both identify and count/quantify localmicrostructures and can also locate them along or amongpolymer chains. If such an experimental technique exists, itmust necessarily be sensitive to the entire structures of mac-romolecular chains. Here, we suggest that the contributionsmade by polymer solutes to the electrical birefringenceobserved for their dilute solutions when subjected to strongelectric fields, or their Kerr effects, are experimental probesof complete polymer chains that are sensitive enough to dis-tinguish their macrostructures.3,4

The reason we want to determine the macrostructures ofpolymers, through identification, quantification, and loca-tion of their constituent microstructures, is because themacrostructures of polymers dictate their overall behaviors.Structure–property relations developed for polymer materi-als that are truly useful and relevant must be based ontheir macrostructures and not simply upon the types andquantities of short-range microstructural elements theyposses. Just as the tertiary and quaternary structures andbiological functions of proteins are determined by their pri-mary sequences of amino acids, so too are the behaviorsand properties of synthetic polymers critically dependenton their macrostructures.

Along with emphasizing that it is the macrostructures ofpolymers, that is, the connectivity of their constituentmicrostructures, which should be the focal point for devel-opment of structure–property relations, and more a impor-tantly, we present evidence that the Kerr effect may beused to probe/determine polymer macrostructures. Themolar Kerr constant, mK of a polymer solute measured indilute solution represents a macroscopic property charac-teristic of the entire chain, like its mean-square end-to-enddistance (<r2>) or radius of gyration (<s2>) and dipolemoment (<l2>). While alterations in the microstructuresof polymers may typically change their dimensions(<r2>,<s2>) or dipole moments (<l2>) by factors of �2to 5, the mKs of small molecules5 (e.g., monomers) rangeover more than four orders of magnitude, and may beeither positive or negative.

Initially4,6,7 to determine if the Kerr effect may be used toprobe/determine polymer macrostructures, we selected andsynthesized styrene/p-bromostyrene (S/pBrS) copolymerswith controlled micro- and macro-structures. S/pBrS copoly-mers were chosen for the following reasons: (1) The dipolemoments of S and pBrS repeat units are quite different; (2)for the same stereosequences, the conformational character-istics, or average randomly coiling conformations, of allS/pBrS copolymers are essentially identical.8 Consequently,

portions of their 13C-NMR spectra potentially sensitive tomicrostructure (i.e., the resonance frequencies of their back-bone CH and CH2 and side chain C1 carbons) are independ-ent of both their comonomer compositions and sequences,as carefully documented in refs. 4 and 7; and (3) conforma-tions that are dependent solely on copolymer stereosequen-ces, but that are independent of their comonomercompositions and sequences, simplify the calculation of

mKs.3,4 The latter two reasons are important, because the

mKs measured for polymers can only be interpreted, interms of the types, quantities, and the locations of theirmicrostructures, by comparison with the mKs calculated forthe corresponding micro- and macrostructural features.

These advantageous features were previously used toexamine S/pBrS copolymers obtained by the brominationof atactic polystyrene (PS) to yield various random orblocky copolymer samples.6,7 From comparison ofobserved and calculated mKs for random S/pBrS copoly-mers, we were able to conclude6 that the original PS sam-ple was nearly ideally atactic. Bromination of atactic PS inpoor, theta, and good solvents produced S/pBrS copoly-mers7 whose comonomer sequences were blocky, random/blocky, and random, respectively, and which could only beconfirmed from comparison of their observed and esti-mated Kerr effects.

More recently,4 the 60% pBrS/40% S triblock copolymersS60-b-pBrS180-b-S60 and pBrs90-b-S120-b-pBrS90 were synthe-sized and their Kerr constants were observed to have similarmagnitudes, but to be, respectively, positive and negative.Also reversible addition-fragmentation chain transfer (RAFT)controlled radical polymerization of random and gradient S/pBrS were conducted and their Kerr constants wereobserved. Comparison with the Kerr constants measured forrandom and blocky S/pBrS samples7 made by brominationof PS in poor, theta, and good solvents and those calculatedfor gradient S/pBrS copolymers strongly suggested that thegradient copolymers did not have atactic stereosequences.

Rather, we found that calculated and observed mKs for ran-dom/statistical and gradient S/pBrS copolymers produced byRAFT polymerizations were only similar when the gradientcopolymers were assumed to have an associated stereose-quence gradient, as illustrated in Figure 1. Only copolymersthat were rich in racemic (r) pBrSApBrS diads on one chainend and rich in SAS diads, with or without a preference formeso (m) diads, on the other chain end yielded mKs as largeas those of S/pBrS copolymers with random/statisticalcomonomer sequences and stereosequences, in agreementwith the experimental mKs.

In this study, we further examined some specifically synthe-sized S/pBrS copolymers. We used both uncontrolled andalternative controlled free-radical polymerization (ATRP) tosee if their gradient samples showed Kerr effects similar tothe gradient samples obtained by RAFT, with largely racemicpBrSApBrS diads. Comparison of the Kerr effect observedfor a random 50:50 S/pBrS copolymer with the Kerr effect

Stereosequences Comonomer Sequences

. . .mmmmmmrmrmrmrmrrrrrrm. . . . . .• • • • � • � � � �• � • •. . .

Vs Vs

. . .mrmmmrrrmrrmmrrmmmrrm. . . . . .• �� • • • • � • � • �. . .

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156 JOURNAL OF POLYMER SCIENCE, PART B: POLYMER PHYSICS 2015, 53, 155–166

of a 50:50 mixture of 80:20 and 20:80 S/pBrS copolymerswas made to learn if the Kerr effect can distinguish betweensamples with polymer chains that all have the same micro-structures from those with a heterogeneous distribution ofmicrostructures, but with the same overall sample averagelocal microstructures. Of course, these samples cannot bedistinguished by NMR or other spectroscopies with short-range sensitivity to microstructures.

In addition, we measured the Kerr constants of severalcopolymer samples with chemical structures very differentfrom S/pBrS copolymers, which were obtained from twocolleagues. Styrene/butadiene multiblock copolymers, withthe same overall composition, but with random and regu-larly alternating block sequences, and ethylene/vinyl acetate(E/VAc) copolymers with the same overall compositions, butwith distinct precise or random placement of comonomerunits and distinct stereosequences were provided by theLee and Bates9 and Hillmyer and coworkers10 groups,respectively.

We also measured the Kerr constants of individual verydilute solutions of isotactic (i) and syndiotactic (s) poly(-methyl methacrylate) (PMMA) and compared them to thatof their mixed solution in two different solvents. At lowconcentrations, stereoregular PMMAs are known to formsoluble complexes in some solvents, but not in others.11

This was done to determine if interactions between macro-molecules could also be successfully probed with the Kerreffect.

In each of the above instances, measured Kerr constantswere able to distinguish between and help identify the dis-tinct macrostructures of and interactions between these co-and homopolymer samples.

Polymer Kerr EffectsThe Kerr effect12 is the birefringence produced in materi-als through application of a strong electric field E. JohnKerr showed that Dn 5 (B/k)E2, where Dn5njj2n?, thatis, the difference in refractive indices along and perpendic-ular to the direction of E, k is the wavelength of light usedto measure the birefringence Dn, and B has become

known as the Kerr constant. Riande and Saiz13 have sum-marized the experimental observation of Kerr constants,and from them, the derivation of molar Kerr constants,

mKs. For all but the most isotropic (nonpolar and mini-mally polarizable) molecules, mKs obtained at infinite dilu-tion may be derived experimentally14,15 from the followingrelation:

mK5 6NAknBð Þ= q n12ð Þ2 e12ð Þ2h i

;

where n, B, q, and e are the refractive index, Kerr constant,density, and dielectric constant of the solution, respectively,all extrapolated to infinite dilution.

The magnitudes and signs of molecular Kerr effects are char-acteristic of the magnitudes and directions of their resultantoverall polarizability tensors, a, and dipole moments, l.Nagai and Ishikawa16 have shown that the molar Kerr con-stant is given molecularly by:

mK5ð2pNA=135Þ ð<lTal>Þ=k2T21ð<aRa0C>Þ=kT� �

;

where < > indicates an average over all conformations of themolecule and is particularly important for flexible macromo-lecules, which can assume a myriad of conformations. Floryand Jernigan17,18 showed how matrix multiplication techni-ques can accomplish the appropriate conformational averag-ing, provided a reliable description of a polymer’sconformational characteristics is available.

The molar Kerr constant of a polymer solute measured indilute solution represents a macroscopic property character-istic of the entire chain, like its mean-square end-to-end dis-tance (<r2>) or radius of gyration (<s2>) and dipolemoment (<l2>). While alterations in the microstructures ofpolymers may typically change their dimensions(<r2>,<s2>) or dipole moments (<l2>) by factors of �2 to5, the mKs of small molecules5 (e.g., monomers) range overmore than four orders of magnitude, and may be either posi-tive or negative.

A microstructural alteration anywhere along a polymerchain may potentially be evident in its NMR spectrum.However, because of its inherent short-range sensitivity,the spectral consequence of such a microstructural altera-tion, that is, chemical shifting of its resonance frequen-cies,1,2 is not sensitive to nor reflects its position orlocation along the chain. Because the molar Kerr constantsof polymers depend on the magnitudes and orientations oftheir overall dipole moment vectors and anisotropicpolarizability tensors, identical or similar microstructuralfeatures located at different positions along the macromo-lecular chain backbone may produce substantially differentoverall mKs, which can be used to distinguish and locatethem. However, they can only be interpreted, in terms oftheir macrostructures, that is, types and the locations oftheir contributing microstructures, by comparison to the

mKs calculated for the assumed corresponding macrostruc-tural features.

FIGURE 1 Illustrations of the random or statistical (stat) and

gradient (grad) S/pBrS copolymer sequences synthesized and

investigated by Kerr effect measurements. Correlated comono-

mer and stereosequence are also shown in poly(S-grad-pBrS)

(Adapted from ref. 4).



RESULTS AND DISCUSSION

Kerr Effects and Macrostructures of S/pBrS CopolymersAlthough initially unexpected from our calculated molar Kerrconstants, and those observed for random and blocky atacticS/pBrS copolymers made by brominating atactic PS in sol-vents of different quality,7 we observed similar mKs for theintimately enchained S/pBrS copolymers synthesized byRAFT copolymerization4 (see Fig. 1 above). As listed in Table1, all RAFT S/pBrS copolymers show closely similar molarKerr constants, irrespective of their comonomer sequences.Based on our previous Kerr effect studies7 of S/pBrS copoly-mers obtained by bromination of atactic PS in good andpoor solvents, we had expected that a gradient sequence ofcomonomers with a similarly atactic stereosequence wouldproduce mKs considerably smaller and somewhat larger,respectively, than those observed for atactic random/statisti-cal and blocky S/pBrS copolymers.

A comparison of experimental and calculated mKs of ran-dom, blocky, and gradient samples of S/pBrS copolymersobtained by brominations of a-PS and RAFT copolymeriza-tions led us to the tentative identification of an unexpectedmacrostructural element/feature introduced during our con-trolled radical RAFT syntheses of intimate S/pBrS copoly-mers, that is, a stereosequence gradient characterized by achanging population of r and m diads from one chain end tothe other, which parallels their gradient comonomersequence (cf. Fig. 1). As the population of pBrS unitsdecreases along the chain, the population of r diads appearsto also decrease. This is a particularly important, result,because in the usual uncontrolled free-radical initiated poly-merizations of S and pBrS, the resulting homopolymers [PSand P(pBrS)] are found to have nearly ideally random stereo-sequences characterized by Pr � Pm � 0.5.19–23

Two random S/pBrS copolymers, both with 50:50 S:pBrScompositions, were also synthesized, one by RAFT and theother by conventional free-radical polymerizations. Much likethe random and blocky S/pBrS copolymers produced by bro-mination in solvents of different quality for PS,7 their thinfilms showed distinct dewetting behaviors. While the randomRAFT S/pBrS film did not dewet from a silica surface after 2days of annealing above Tg at 150 �C, the random S/pBrSfilm prepared from samples synthesized by free-radical poly-merization did (See Fig. 2). This suggests that, as previouslyobserved for random and blocky samples of atactic S/pBrScopolymers,7 the micro- and macrostructures of these sam-ples differ. In the case of the uncontrolled and controlled(RAFT) free-radically synthesized 50:50 random copolymers,this difference can only originate from different locations oftheir stereosequences.

Racemic (r) pBrSApBrS diads substantially populate8 theextended trans–trans backbone conformation, which placesboth brominated side-chain phenyl rings on opposite sidesof the extended backbone plane, with both up or both down,as demonstrated in Figure 3. In contrast, in meso (m)pBrSApBrS diads the extended trans–trans backbone confor-mation is not substantially populated, while those conforma-tions that are more heavily populated are not extended withparallel brominated phenyl rings either on the same oropposite sides of the backbone plane.

Our Kerr effect observations strongly suggest that RAFT syn-thesized copolymers do and the uncontrolled conventionallysynthesized free-radical copolymers do not have predomi-nantly racemic pBrSApBrS diads. pBrSApBrS diads, whichare substantially populated by the trans–trans backbone con-formation, tend to place both brominated phenyl rings onopposite sides of the backbone plane in a position to interact

TABLE 1 Comparison of Kerr Constants Measureda for S/pBrS Copolymers Synthesized by RAFT and ATRP Controlled Radical

Polymerizations

Sample Name

Mole fraction of

pBrS in S/pBrS

Copolymer

Method of

Comonomer

Addition

Comonomer

Addition

Rate (mL/min)

Slopes of Solution Kerr

Constants 31016, V22 m,

Versus Concentration

Relative

mKs

Poly (statistical-S/pBrS)

ATRP Targeted feed ratio: 50:50 Simultaneous NA 2 0.9

S-50-I RAFT 50% Simultaneous NA 2.8 1.25

S-50-IIFRP (Targeted feed ratio: 50:50) Simultaneous

uncontrolled, AIBN

NA 2.7 1.16

Poly (“gradient”-S/pBrS)

ATRP Targeted feed ratio: 50:50 Gradient with syringe pump 0.002 1.2 0.5

G-48-I RAFT 48% Gradient with hand syringe 0.014 2.2 1.0

G-47 RAFT 47% 00 0.025 2.5 1.16

G-35 RAFT 35% 00 0.007 2.7 1.16

G-48-II RAFT 48% Gradient with syringe pump 0.014 2.6 1.25

G-32 RAFT 32% 00 0.033 2.3 1.06

a Measured in 1,4-dioxane (>99% purity) solutions (1–3 wt %) at 293 K.



POLYMER SCIENCE

strongly with the silicon surface. So possibly, as observed,the RAFT random copolymer film should be stickier. Clearly,the adherence of S/pBrS films to silicon substrates dependsnot only upon their comonomer sequences (blocky stickierthan random)7 but also observed here for random copoly-mers, also upon their stereosequences, with r pBrSApBrSdiads apparently stickier than m pBrSApBrS diads. Thismicro- and macro-structural detail cannot be obtained fromshort-range spectroscopic probes, such as 13C-NMR, which iscurrently the method of choice for characterizing the micro-structures of polymers.

To further examine the suggestion that in the controlledRAFT synthesis of S/pBrS copolymers with a gradient como-nomer sequence a correlated stereosequence gradient wasintroduced,24–26 we used ATRP27 to obtain random and gra-dient samples. ATRP, is known to yield polymers with atacticstereosequences similar to conventional uncontrolled freeradical polymerization, with the radical nature of propaga-tion yielding equal m and r addition of monomers.28,29 Thus,we assume that both gradient and random/statistical S/pBrScopolymers obtained by ATRP are atactic. We measured theirmolar Kerr constants (see Fig. 4), and present (in bold) andcompare them in Table 1 to the Kerr constants measured forthe RAFT S/pBrS copolymers.

Unlike the RAFT samples, the gradient S/pBrS copolymerobtained by ATRP has a much smaller Kerr constant thanthe random S/pBrS copolymer obtained by ATRP, asexpected if both have atactic stereosequences (Also see pre-vious discussion of atactic random and blocky S/pBrScopolymers obtained by bromination of atactic PS in solventsof different quality7). In addition, though not shown here,both ATRP produced 50:50 S:pBrS films began dewettingfrom silicon surfaces almost immediately after annealingabove their Tg at 150 �C (see Fig. 2 and related discussion).

However, the gradient sample remained on the silicon sur-face much longer than the random sample. These film dewet-ting observations are consistent with those seen for atacticrandom and blocky S/pBrS samples obtained by brominationin solvents of different qualities for PS.7 The comparison ofboth Kerr constants and film dewetting behaviors reinforcesthe conclusion that in the RAFT and ATRP syntheses ofS/pBrS copolymers enchainment of r pBrSApBrS diads isand is not preferred, respectively, over their m counterpart.

In fact, very recently Ishitake et al.26 have demonstrated bymeans of RAFT copolymerization that methacrylic acid(MAA) homo- and co-polymers possessing a stereosequencegradient may be achieved. This was accomplished throughcopolymerization with bulky esters of MAA, such as triphe-nylmethyl methacrylate (TrMA), which react more slowlythan MAA to produce MAA/TrMA copolymers with a gradi-ent comonomer sequence. The MAA- and TrMA-rich sequen-ces were created by disparate comonomer reactivity ratiosand adjustment of the comonomer feeds. The stereosequen-ces in the TrMA- and MAA-rich regions were found to belargely isotactic and atactic, respectively. Furthermore, meso(m) TrMA diads were preferentially formed, resulting inMAA/TrMA copolymers with gradients in both comonomersequence and stereosequence. According to Ishitake et al.,26

“. . .the stereogradient structure is a result of the propaga-tion–depropagation equilibrium, which can convert a lessthermodynamically stable growing terminus with a racemic

FIGURE 2 Dewetting of random 50:50 S:pBrS copolymer films

made by controlled RAFT (top) and unconctrolled free-radical

(bottom) polymerizations.

FIGURE 3 Along backbone end-view (bottom) and �45� from

full frontal-view (top) of a r-pBrSApBrs diad.



(r) conformation into the more stable meso (m) form.”Finally, removal of the triphenylmethyl groups producedMAA homopolymers with a stereosequence gradient that var-ied from syndiotactic to isotactic (i.e., mm5 11–100%) fromone end of the chains to the other.

The fact that Kerr effect measurements are not only sensitiveto comonomer stereosequences, but also their locationsalong the polymer chains suggest the promise of this tech-nique to further probe the mechanistic underpinnings of pol-ymerizations capable of achieving stereocontrol. Because ofthis capability, we observed that RAFT polymerizations car-ried out under conditions that led to gradient S/pBrS copoly-mers also had a gradient of stereosequences along the chain.Although invisible to NMR, this Kerr effect observation indi-cated stereo-control during a controlled radical polymeriza-tion without external additives (e.g., Lewis acids). This effectis surprising, and serves as a perfect example of the promiseof Kerr effect measurements for elucidating specific charac-teristics of polymerization mechanisms undetectable bymore traditional techniques.

We will further exploit the Kerr effect to probe RAFT gradientcopolymerizations. Gradients of various overall comonomerratios will be prepared to investigate if the stereosequencecontrol is dependent on copolymer feed and/or copolymercomposition. Additionally, the percentage of racemic and mesodiads present in polymers prepared by radical polymerizationis known to depend on polymerization temperature. We willconduct RAFT polymerizations of S and pBrS at temperaturesranging from room temperature to 110 �C by using initiatorsand RAFT agents amenable to the chosen temperatures.

To further confirm the ability of Kerr effect measurements toprovide information regarding stereosequence control andlocations along polymer chains, we will prepare copolymers

with well-defined gradients ensured by the slow addition ofLewis acids known to interact with methacryloyl monomers,thereby leading to stereocontrol. By purposely installing ster-eosequences at specific locations, we will be able to comparethe observed mKs of gradient copolymers of known stereose-quences to their calculated values.

We also measured the Kerr constants for 50:50, 20:80,80:20, and an equal mixture of the 20:80 and 80:20 randomatactic S:pBrS copolymers obtained by conventional free rad-ical polymerization to see if the 50:50 and equal mixture of20:80, and 80:20 random S:pBrS copolymers have distinctKerr constant as the data shown in Figure 5 suggests theyshould. The 50:50 copolymer showed a Kerr constant largerthan that of an equal mixture of the 20:80 and 80:20 copoly-mers in agreement with the expected Kerr constants shownin Figure 5. Thus, it appears the Kerr effect can distinguishbetween samples with polymer chains that all have the samemicrostructures from those with a heterogeneous distribu-tion of microstructures, but with the same overall sampleaverage local microstructures, which of course cannot be dis-tinguished by NMR or other spectroscopies with short-rangesensitivity to microstructures.

FIGURE 4 Kerr constants of PS (commercial), poly(random-

S/pBrS), and poly(“gradient”-S/pBrS) by ATRP as measured on

(1–3 wt %) 1,4-dioxane (>99% purity) solutions at 293 K.

FIGURE 5 Comparison of mKs (31021 cm7 SC22 mol21)

observed and calculated for atactic S/pBr copolymers made by

bromination of a-PS.6 x, c, and Pr are the number of repeat

units (200) and the fractional contents of pBrS units and race-

mic or r-diads, respectively.



POLYMER SCIENCE

Kerr Effects and Macrostructures of Additional PolymersCan the interactions/associations between polymers bedetected by the Kerr effect? Kerr constants were measuredfor separate and combined solutions of i- and s-PMMAs insolvents where they do (tetrahydrofuran (THF)) and do not(Dioxane) form 2:1 s-PMMA:i-PMMA complexes.11 In thecomplexing solvent, the Kerr constant observed for a 2:1 s-PMMA:i-PMMA mixture was very different from a 2:1weighting of the Kerr constants observed for neat s- and i-PMMAs. On the other hand, in a noncomplexing solvent theKerr constant observed for a 2:1 s-PMMA: i-PMMA mixturewas very similar to a 2:1 weighting of their neat Kerr con-stants observed in this solvent. This provides a clear demon-stration of the sensitivity of the Kerr effect to stronglyinteracting/complexing polymers in solution.11

Recently, Lee and Bates9 synthesized random and alternat-ing multiblock copolymers of styrene and butadiene (S/B)that are illustrated in Figure 6. Aside from their overallcompositions, NMR was unable to differentiate betweentheir random and alternating block sequences. Their Kerrconstant measured in dilute dioxane solutions wereobserved to be distinct, as can be seen in Figure 6. Sowhile NMR does not distinguish between samples with ran-dom and with regularly alternating multiblock sequences,the Kerr effect is clearly able to. “Precision linear vinyl ace-tate/ethylene (VAE) copolymers containing acetoxy groupson precisely every eighth backbone carbon were synthe-

sized by ring-opening metathesis polymerization (ROMP)of racemic 3-acetoxycyclooctene (3AcCOE) and subsequenthydrogenation. The use of enantiomerically pure 3AcCOEresulted in an optically active polyalkenamer that affordedisotactic precision VAE materials after hydrogenation. Incontrast, analogous linear VAE copolymers derived fromROMP2hydrogenation of racemic 4- or 5-acetoxy cyclooc-tenes were regioirregular.”10

Kerr constants were measured for the precise and randomVAE copolymers that are atactic and precise VAE copolymersthat are atactic or isotactic, all having the same comonomercomposition. As seen in Figure 7, atactic precise regioregularand atactic random regioirregular VAE samples have thesame Kerr constants, while for the regioregular samples theprecise isotactic sample has a Kerr constants of oppositesign, with a magnitude nearly 10-fold greater than the atac-tic precise sample.10 This large difference is not likely due tothe optical activity of the precise isotactic sample, which hasa nearly 0� (E5 0 volts) optical rotation. Thus, though NMRor optical activity observations cannot, Kerr effect observa-tions can easily distinguish the isotactic and atactic regiore-gular precise VAE samples of Hillmyer and coworkers10 Onceagain this emphasizes that the sensitivity of the Kerr effectsis sufficient to readily identify longer range polymer micro-structures and their locations along the chain to delineatecomplete polymer macrostructures.

In each of the above instances, measured Kerr constantswere able to distinguish between and help identify the dis-tinct macrostructures of and interactions between these co-and homo-polymers.

Finally, to increase the practicality of characterizing syntheticpolymer macrostructures, we suggest30 coupling of NMRspectroscopy1,2 with Kerr effect observations. Although notfor the S/pBrS copolymers discussed here, NMR can usuallyreveal the types and amounts of short-range microstructurespresent in synthetic polymers. Kerr effect observations canthen be used to locate the NMR-derived microstructures

FIGURE 6 Structures and Kerr constants of 0.1 g/dL toluene

solutions of styrene/butadiene multiblock copolymers with ran-

dom and regularly alternating blocks.9

FIGURE 7 Kerr constants of 0.1 g/dL dioxane solutions of E/

VAc samples.10



along the polymer chains. This is achieved by comparison ofobserved molar Kerr constants to those calculated for differ-ent distributions/locations of constituent microstructuresidentified by NMR. The distribution of microstructures usedto calculate an mK in agreement with the observed value isthen identified as its likely macrostructure.

Not using the 13C-NMR-Kerr effect combined approachwould require the calculation of Kerr constants for all pos-sible macrostructures and comparing them to the valueobserved. Because the numbers of distinct synthetic poly-mer macrostructures are astronomically large, thisapproach is not practical. We must instead reduce thepotential macrostructures to a manageable number, and13C-NMR can help us achieve this by identifying and quanti-fying the constituent short-range microstructures that arepresent. With this information in hand, we then move themaround to locate them at different positions along the poly-mer chain. The Kerr constants expected for each of thismuch more manageable number of polymer macrostruc-tures are calculated, compared with the observed value,and, when they agree, are identified as the (those) mostlikely macrostructure(s).

CONCLUSIONS

In summary, we have called attention to the importance ofrecognizing that the macrostructures of synthetic polymersare critical to understanding their behaviors, and so theircharacterization is important. Only a probe that is similarlydependent on the complete macrostructures of polymers canbe used to characterize them. It appears that Kerr effectsmeasured in dilute polymer solutions may be sufficientlysensitive to not only determine the types and quantities ofmicrostructures that are present but also to locate their posi-tions along their macromolecular backbones, thereby allow-ing a more complete description of their macrostructures. Inlight of the many recent developments31 in polymerizationsthat purportedly produce polymers with elaborate and pre-cise architectures, the ability to experimentally determineand verify their expected macrostructures becomes evenmore urgent.

For example, a recent paper “How Far Can We Push PolymerArchitectures”32 describes the tour de force synthesis of the“bottle brush” polymer shown in Figure 8. The authors state“With this study the frontiers in polymer synthesis, molecu-lar analysis, and three-dimensional architectures of polymers

FIGURE 8 Polymer structures 4(c,d) and 5(c,d) including representative AFM height micrographs of 4d (top left) and 5d (top right)

(scale bar 5 50 nm). Schematic representation of the polymer structures on the mica surface (bottom) (From P. J. M. Stals et al., J

Am Chem Soc, 2013, 135, 11421–11424, with permission from the American Chemical Society).



POLYMER SCIENCE

are pushed forward, while at the same time the limitationsin this endeavor are made clear.

Although all analytical results are in agreement with thestructures assigned to structures 4 and 5 (See Fig. 8), itshould be noted that their syntheses is approaching the lim-its of today’s polymer synthesis and analysis techniques.Hence, deviations in end groups by transfer processes andthe presence of small amounts of homo- and co-polymerscannot be excluded, while complete assignment of the NMRspectra of our brush polymers is impossible as well.” Thismeans that the tacticities of their constituent block copoly-mers, numbers, lengths, and distributions of grafted n-butylacrylate brush bristles, and the degree and distribution offunctionalized protected 2-(trimethylsiloxy)ethyl methacry-late units in the bottle brush tail, which upon UV exposurepermits intramolecular hydrogen-bonding and self-assembly,remain uncharacterized. In other words, the macrostructureof this tour de force example of macromolecular architectureremains incompletely characterized, because of the limita-tions of conventional analytical techniques. Kerr effect exami-nation of the intermediate products of their syntheses wouldaid in their characterization and possibly lead to characteri-zation of the complete macrostructure of the final bottlebrush polymer product.

EXPERIMENTAL

MaterialsStyrene (Aldrich, 99%) and 4-bromostyrene (Aldrich, 98%)were passed through a column of basic alumina before use.2,20-Azobis(isobutyronitrile) (AIBN) (Aldrich, 98%) wasrecrystallized from ethanol. 2-(1-Carboxy methylethylsul-fanyl-thio-carbonylsulfanyl)22-methylpropionic acid (CMP)and 2-dodecylsulfanylthio-carbonyl-2-methylproprionic acid(DMP) chain transfer agents (CTAs) were prepared as previ-ously reported. 1,3,5-Trioxane (Acros, 99.5%), N,N-dimethyl-formamide (DMF) (Aldrich, 99.9%), THF (Malinckrodt, 99%),anisole (Aldrich, 99%), and methanol (Aldrich, 99%) wereused as received.

Instrumentation and AnalysesNuclear Magnetic ResonanceProton nuclear magnetic resonance spectroscopy (1H NMR)was used to evaluate polymerization reaction kinetics and toconfirm the chemical composition of the resulting copoly-mers. The spectra were obtained with a Bruker Advance 400Spectrometer operating at 400 MHz; the analyses were per-formed in CDCl3. Inverse gated decoupling 13C NMR spec-troscopy was used to characterize the chemical compositionof the copolymers. The spectra were obtained with a JEOLSpectrometer operating at 500 MHz; the analyses were per-formed from concentrated solutions of the compoundsin CDCl3.

Elemental AnalysisElemental analysis (EA) was employed as a measure ofchemical composition for the copolymers synthesized.

Elemental analyses were performed by Atlantic Microlab,Atlanta, GA.

Size Exclusion ChromatographySize exclusion chromatography (SEC) was used to character-ize the molecular weights of the S/pBrS copolymers. Theinstrument was equipped with a Waters 2695 separationsmodule, a light scattering detector (MiniDawn, Wyatt Tech-nology Co.) and a differential refractive index detector (Opti-lab Rex, Wyatt Technology Co.), and used a Styrogel HR 4column. Conventional calibration was done using nine PSstandards from Fluka. Samples were filtered through 0.2-mmPTFE syringe filters. THF was used as an eluent solvent atthe flow rate of 0.3 mL min21 at room temperature. Theresults are reported as number average molecular weight(Mn) and polydispersity (Mw/Mn).

Polymer SynthesesPS-b-pBrS-b-PS TriblocksAn example synthesis of the triblock copolymers by RAFTpolymerization of styrene (S) and p-bromostyrene (pBrS)with CMP was conduced as follows. S (4.09 g, 39.3 mmol),CMP (55.5 mg, 0.196 mmol), AIBN (13 mg, 0.079 mmol), tri-oxane (110 mg, internal NMR standard), and DMF (1.0 mL)were placed in a sealed 20 mL glass vial equipped with amagnetic stir bar. The air space above the reaction solutionwas purged with nitrogen for 10 min, and the solution wasthen sparged with nitrogen for an additional 15 min. Thevial was placed in a preheated reaction block at 75 �C.Kinetic samples were removed periodically via a nitrogen-purged syringe. Monomer conversion was determined by 1HNMR spectroscopy and terminated at 16 h, at 57% conver-sion. The polymer was diluted in THF and precipitated incold MeOH (32), filtered, and vacuum dried at 40 �C(2.13 g). Molecular weight was determined by SEC (Mn 5

12,700 g/mol, Mw/Mn5 1.06): PSty59-b-PSty59.

An example RAFT copolymerization of a PS macroCTA withpBrS was performed as follows. PS macroCTA (0.48 g, 0.038mmol), pBrS (2.80 g, 15.3 mmol), AIBN (2.5 mg, 0.015mmol; 0.45 mL of 5.5 mg/mL AIBN/DMF stock), trioxane(85 mg, internal NMR standard), and DMF (2.0 mL) wereplaced in a sealed 20 mL glass vial equipped with a mag-netic stir bar. The air space above the reaction solution waspurged with nitrogen for 10 min, and then the solution wassparged with nitrogen for an additional 15 min. The vial wasplaced in a preheated reaction block at 75 �C for 16 h. Thepolymerization solution was quenched in an ice bath. To iso-late the copolymer, the reaction solution was diluted withTHF, precipitated in cold MeOH, filtered, and vacuum driedat 40 �C (1.61 g). Molecular weight of the isolated/driedpolymer was determined by SEC (Mn 5 45,400 g/mol, Mw/Mn 5 1.2): S59-b-pBrS79-b-pBrS79-b-S59.

P(S-stat-pBrS) Copolymers—ConventionalAn example conventional (uncontrolled) statistical copoly-merization (stat) of S and pBrS was performed as follows. S(1.36 g, 13.1 mmol), pBrS (2.40 g, 13.0 mmol), AIBN(8.7 mg, 0.053 mmol), and trioxane (98.2 mg, internal NMR



standard) were placed in a 20 mL glass vial equipped with amagnetic stir bar. The air space above the reaction solutionwas purged with nitrogen for 10 min, and the solution wasthen sparged with nitrogen for an additional 15 min. Thesolution was placed in a preheated reaction block at 75 �Cand proceeded for 2 h. To isolate the copolymer, the reactionsolution was diluted with THF, precipitated into cold MeOH(32), filtered, and vacuum dried at 40 �C (1.21 g). Molecularweight of the isolated polymer was determined by SEC((Mn 5 47,920 g/mol, Mw/Mn5 1.7).

P(S-stat-pBrS) Copolymers—RAFTAn example RAFT statistical copolymerization of S and pBrSwas performed as follows. S (1.36 g, 13.1 mmol), pBrS(2.40 g, 13.0 mmol), AIBN (8.6 mg, 0.052 mmol), DMP(47.8 mg, 0.131 mmol), trioxane (99 mg, internal NMRstandard), and DMF (1 mL) were placed in a 20 mL glassvial equipped with a magnetic stir bar. The air space abovethe reaction solution was purged with nitrogen for 10 min,and then the solution was sparged with nitrogen for an addi-tional 15 min. The solution was placed in a preheated reac-tion block at 75 �C. Kinetic samples were removedperiodically via a nitrogen-purged syringe. Monomer conver-sion was determined by 1H NMR spectroscopy, comparingthe area of the anisole and trioxane signals to the vinyl pro-tons of the residual monomer (8 h, 64%). To isolate thecopolymer, the reaction solution was diluted with THF, pre-cipitated into cold MeOH (32), filtered, and vacuum dried at40 �C (0.76 g). Molecular weight of the isolated polymer wasdetermined by SEC (Mn5 9296 g/mol, Mw/Mn 5 1.1).

P(S-grad-pBrS) Copolymers—RAFTGradient copolymerization of S and pBrS were synthesizedvia RAFT with varying ratios of pBrS (Table 1) using either afree-syringe (hand syringe) (G-48-I, G-47, G-35) or a syringepump (G-48-II, G-32) method. The polymerizations wereconduced as follows. A stock solution of pBrS was purgedwith nitrogen for 30 min before the reaction. S (1.37 g, 13.1mmol), AIBN (4.4 mg, 0.027 mmol), DMP (24.1 mg, 0.066mmol), trioxane (85.9 mg, internal NMR standard), and DMF(1.0 mL) were placed in a sealed 20 mL glass vial equippedwith a magnetic stir bar. The air space above the reactionsolution was purged with nitrogen for 10 min, and then thesolution was sparged with nitrogen for an additional 15 min.The vial was placed in a preheated reaction block at 75 �C.The pBrS was then either drawn into a purged 1 mL syringeand inserted into the septum of the reaction vial for thefree-syringe method or a purged syringe of pBrS wassecured on a syringe pump with a 22-gauge needle insertedinto the septum of the vial for the syringe pump method.pBrS was then added at various rates over a period of 2 hand stirred for an additional 3 h after addition was complete.To isolate the copolymer, the reaction solution was dilutedwith THF, precipitated into cold MeOH (32), filtered, andvacuum dried at 40 �C (1.14 g). Molecular weight of the iso-lated polymer was determined by SEC (G-48-I Mn 5

12,850 g/mol, Mw/Mn5 1.2, G-47 Mn 513,020 g/mol, Mw/Mn 51.2, G-35 Mn 527,202 g/mol, Mw/Mn 51.13) or a

syringe pump (G-48-II Mn 57057 g/mol, Mw/Mn 51.1, G-32 Mn 58074 g/mol, Mw/Mn 51.2).

P(S-random-pBrS) Copolymers—ATRPS (>99%, Aldrich) was passed through basic alumina columnand pBrS (>99%, Aldrich) was distilled (b.p.5 88 �C at 15mmHg) before use. Phenylethyl bromide, 1-PEBr (>99%,Aldrich), Cu(I)Br (>99%, Aldrich), N,N,N0,N00,N00-pentamethyl-diethylenetriamine, PMDETA, (>99%, Aldrich), and diphenylether (�99%, Aldrich) were used as received.

A typical procedure of ATRP was performed for Randomcopolymerization of S and pBrS.33,34 Cu(I)Br (62.5 mg, 0.435mmol) was placed in a 25-mL Shlenk flask equipped with amagnetic stir bar under ambient conditions. PMDETA (0.435mmol, 90 mL), monomers S (21.75 mmol, 2.25 mg), and pBrS(21.75 mmol, 3.9 mg) were added sequentially and the mix-ture was stirred for 5 min at 25 �C under N2. Initiator, 1-PEBr (0.87 mmol, 12 mL) was added. The mixture wasdegassed by three freeze-pump-thaw cycles. The flask wasplaced in a preheated (100 �C) oil bath. ([Monomer]:[1-PeBr]:[Cu(I)Br]:[PMDETA]5 100:0.2:1:1) After 24 h, thepolymerization reaction was stopped by exposing the reac-tion mixture to the air. The polymer was dissolved in THFand was introduced to 250 mL Erlenmeyer flask filled withbasic alumina in order to remove metal catalyst, Cu(I)Br. Thebeaker was placed in orbital shaker for 1 day. Polymer wasfiltered, the excess amount of THF was removed by rotaryevaporation then the polymer was precipitated into coldMeOH (310), filtered, and vacuum dried at 25 �C. Precipita-tion was repeated until a white polymer powder was pro-duced. Molecular weight of the isolated polymer wasdetermined by SEC (Mn5 159,773 g/mol, Mw/Mn 5 1.25).

Synthesis of Poly (“gradient”-S/pBrS)—ATRPGradient copolymers were prepared via a semi-batch copoly-merization using ATRP, as described by Matyjaszewski et al.35

Cu(I)Br (62.5 mg, 0.435 mmol) was placed into a 25-mLShlenk flask equipped with a magnetic stir bar. PMDETA(0.435 mmol, 90 mL), solvent diphenyl ether36 (2.5 mL, Vsol-vent/Vstyrene5 1/1), and S (21.75 mmol, 2.25 mg) were added,respectively, and then the mixture was stirred for 5 minunder N2.

37 Initiator 1-PEBr (0.87 mmol, 12 mL) was added.The mixture was degassed by three freeze-pump-thaw cyclesthen sealed. The flask was placed in a preheated (100 �C) oilbath. ([Monomer]:[1-PeBr]:[Cu(I)Br]:[PMDETA]5 100:0.2:1:1)Simultaneously, pBrS was introduced into a 25 mL reactiontube and degassed by three freeze-pump-thaw cycles. Then,pBrS was transferred into an airtight syringe and fixed to asyringe pump. The syringe pump was programmed to deliver2.80 mL at a rate of 2 mL/min. The reaction was stirred for24 h after the pBrS addition was completed. The total reactiontime was 46 h and 30 min. The polymerization reaction wasstopped by exposing the reaction mixture to air. The polymerwas diluted with THF and was introduced into a 250 mLErlenmeyer flask filled with basic alumina in order to removethe metal catalyst, Cu (I) Br. The beaker was placed in anorbital shaker for one day. Polymer solution was filtered, the



POLYMER SCIENCE

excess amount of solvent was removed by rotary evaporation,then the polymer was precipitated into cold MeOH (310), fil-tered, and vacuum dried at 25 �C. Precipitation was repeateduntil a white polymer powder was produced. Molecularweight of the isolated polymer was determined by SEC(Mn5 253,330 g/mol, Mw/Mn5 1.03).

Kerr Effect Measurements and CalculationsA schematic diagram of the components essential for Kerreffect measurements is presented in Figure 9. A state-of-the-art Kerr effect instrument has recently been constructed inour laboratory. We purchased a custom built Kerr effectinstrument from Hinds Instruments (Hillsboro, OR). The lightsource is a 5 mW HeANe laser, which passes through apolarizer and photoelastic modulator and the polarizer isoriented 45� relative to the photoelectric modulator or PEM.The detection system, explained in detail elsewhere,38 con-sists of two Si photodetectors behind either a 245 or 0�

polarizer to measure the magnitude and orientation of theretardation in the sample.

The sample cell consists of two parallel, stainless steel elec-trodes 15 cm in length, with a cell gap of 2.5 mm maintainedby Teflon spacers. The cell windows are made of low-birefringence glass supplied by Hinds Instruments. Theinstrument contains a high voltage source with an analogcontrol system to obtain the high electric field strengths.Raw data is recorded on a computer through a custom con-trol program supplied by Hinds Instruments, and, for a givensample, data points are collected every 100 ms. The perti-nent data recorded for Kerr constant calculations are theretardation (Dn) and voltage.

The Kerr effect of a given copolymer sample was measuredat a series of different weight fractions in solution (e.g.,C5 0.5, 1.0, and 2.0 w/w %). The Kerr constant of the solu-tion, B, is calculated from the relationship Dn5 kBE2, wherek 5 633 nm and was averaged over the values observed forapplied voltages of 10–12 kV. Because the triblock and gradi-ent/random S/pBrS samples under consideration here havesimilar compositions, we expect refractive index, density, anddielectric constant to remain approximately constantbetween sample pairs. As such, the ratio of mKs for a samplepair depends on the ratio of slopes of their B versus C plots.

In addition, a refractometer operating at the same wave-length as the Kerr-Effect instrument and a dielectric meter

are also necessary components for measuring refractive indi-ces and dielectric constants of the dilute polymer solutions.These are necessary to evaluate their absolute molar Kerrconstants and have been obtained to accompany our Kerreffect instrument. Measurements of the Kerr effect weremade on polymer solutions (0.5–3% w/w) in 1,4-dioxane(>99% purity from Sigma-Aldrich), THF (>99% purity fromSigma-Aldrich), or Toluene (>99% purity from Sigma-Aldrich) at 293 K.

In a few cases where the Kerr effect of the same sample inTable 1 was repeatedly measured, the Kerr constants derivedfrom them varied no more than �10%.

In the calculation of molar Kerr constants, we considered S/pBrS copolymers with 300 total comonomer units. For eachdistinct comonomer composition, comonomer sequence, andtacticity or stereosequence a sample of at least 50 copolymerchains were generated using a commercial random numbergenerator and our own FORTRAN algorithms. Each copoly-mer chain was built one comonomer unit at a time, withaccount taken of both the type of comonomer added andwith which stereosequence (m or r diad, relative to the pre-vious unit added). Further details of the mK calculations forS/pBrS copolymers can be found in refs. 3, 4, 6, 7, and 13.

Film DewettingDewetting studies of thin S/pBrS copolymers films were per-formed on single-side-polished, 300-mm thick, small pieces(13 1 cm2) of silicon wafers which were covered with an�1 nm self-assembled monolayer (SAM) of 1H,1H,2H,2H-per-fluoro-decyltrichlorosilane. Decoration of the SAMs on siliconwafers was performed as described previously.7,39 Sliconwafers were placed into an ultraviolet/ozone cleaner for 30min in order to produce AOH groups on the surface. A smalldrop of perfluoromethyldecalin was placed on the bottom ofa Petri dish and the silicon wafer was placed above the per-fuoro source. The Petri dish was closed and kept at roomconditions for 20 min. The wafer was taken out of the Petridish, washed with ethanol and dried with nitrogen.39 TheSAM decorated silicon sample thicknesses were measured byellipsometry before spin-casting the S/pBr copolymer filmsonto them in order to be sure that the sample surfaces weredecorated with the SAM.

Copolymer films were placed on the silicon wafers decoratedwith SAM as described previously.7 Thin S/pBrS copolymer

FIGURE 9 Schematic of a typical Kerr effect Instrument.



films were spun-cast on glass substrates. They were thenfloated onto the surface of a deionized water bath, andplaced onto the SAM decorated silicon wafers. After dryingovernight, the sample thicknesses (�35 nm) were measuredby ellipsometry and annealed under a nitrogen atmosphereat T2Tg 5 35 �C–150 �C.15 Dewetting of the S/pBrS copoly-mer films was monitored by optical microscopy.

ACKNOWLEDGMENTS

We are grateful to the National Science Foundation for financialsupport [(A. E. Tonelli), DMR-0966478], to the Army ResearchOffice for a DURIP equipment grant [(J. Genzer and A. E. Tonelli)#53583 CH-RIP] to build a Kerr effect instrument, and to theHinds Instrument Co., Hillsboro, OR for constructing our Kerreffect instrument. We are indebted to Marc Hillmyer for provid-ing several regioregular and irregular atactic and isotactic VAEcopolymer samples, with random or precise comonomersequences. We also thank Frank Bates for providing us withsamples of random and regularly alternating S/B multiblockcopolymers.

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Beyond Microstructures: Using the Kerr Effect to …ing polymer microstructures uses high field, high resolution 13C-nuclear magnetic resonance (NMR) spectroscopy observed in solution.

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